I took my first investing class as a teenager, and one moment stands out in my memory. A fellow student asked the instructor, a stockbroker, about dividends.

"Dividends?" he asked. "I'm trying to make my clients wealthy. You don't do that waiting for tiny checks in the mailbox every quarter."

Even then, I had enough horse sense to know he was wrong. Paying attention to dividends is exactly how you become wealthy over time.

Wharton professor Jeremy Siegel offered a wonderful discovery in his book The Future for Investors. The greatest long-term returns typically don't come from the most innovative companies, or even companies with the highest earnings growth. They come from companies that happen to crank out dividends year after year. Simply put, since the 1950s, "the portfolios with higher dividend yields offered investors higher returns."

Market commentary regularly centers on price gyrations, yet dividends have historically accounted for more than half of total returns.

Reinvest those dividends, and it's even greater. Take General Mills (NYSE: GIS) for example. Since the late 1960s, General Mills' share price has increased 3,400%. But add in reinvested dividends, and total returns jump to an astounding 14,700%:

Gis

Source: Capital IQ, a division of Standard & Poor's.

There's no ambiguity here: Over time, General Mills' share appreciation alone has paled in importance to the power of its reinvested dividends. The results are similar for competitors Kraft (NYSE: KFT) and ConAgra (NYSE: CAG); Reinvested dividends skew both companies' total long-term returns dramatically higher. If you're a long-term shareholder, don't worry about daily share wobbles. Devote your attention those dividend payouts, and your commitment to reinvest them.

And how do General Mills' dividends look? A sentence from the company's website says it all: "General Mills and its predecessor firms have paid dividends, uninterrupted and without reduction, for 112 years." Very few companies can claim anything close. Its current yield, 3.2%, is comfortably above the market average. Over the past five years, dividends have used up an average of 50% of free cash flow -- a fairly healthy ratio that leaves room for both error and growth. General Mills has been one of the top dividend stocks to own over the long term and should stay that way for the foreseeable future.

To earn the greatest returns, get your priorities straight. What the market does is less important than what your company earns. What your company earns is less important than how much it pays out in dividends. And what it pays out in dividends is less important than whether you reinvest those dividends.

Fool contributor Morgan Housel doesn't own shares in any of the companies mentioned in this article. Follow him on Twitter @TMFHousel. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.